The Estimation Method of Inference Functions for Margins for Multivariate Models

An estimation approach is proposed for models for a multivariate (non-normal) response with covariates when each of the parameters (either a univariate or a dependence parameter) of the model can be associated with a marginal distribution. The approach consists of estimating univariate parameters from separately maximizing univariate likelihoods, and then estimating dependence parameters from separate bivariate likelihoods or from a multivariate likelihood. The analysis of this method is done through the theory of inference or estimating functions, and the jackknife method is proposed for obtaining standard errors of the parameters and functions of the parameters. The approach proposed here make a large contribution to the computational feasibility of carrying out inference with multivariate models. Examples illustrate the approach, and simulation results are used to indicate the efficiency.